Abstract In this paper, we present a new approach to deal with the
translation-invarint and scale-invarint problem of discrete wavelet
transform. We first adaptively renormalize the original signal by an
orthonomal scale function and the first order and second order moments
of the signal. This procedure can be accomplished by using a
changeable filter, whose impulse response is adaptively selected from
a "mother mask", prepared before. Then, we decompose the renomalized
signal by using Mallat*s algorithm, and the coefficients of this
adaptive wavelet transform, a as we prove, are both translation- and
scale-invariant. We also demonstrated that these coefficients, which
are called adaptive wavelet invariant moments (AWIM), can be
approximately computed by an efficient algorithm. Finally, experiment
results for 2-dimension digital images are given. Key Words: wavelet
transform, translation-invariance, scale-invariance, wavelet invariant
moments.